Blame azrhey

[swestrup]

She posted a physics conundrum in her journal, so I've decided to post one of my favorites:

A swimming pool full of water has a row-boat floating in it. The rowboat is just barely managing to float (the boats sides are almost underwater) because a large lead weight is sitting in the boat. The slightest wave will spill water into the boat, causing it and its cargo to sink to the bottom of the pool. If this happens, after all the waves have settled down, will the level of the pool have gone up, gone down, or stayed the same?

Comments

[denizsarikaya.livejournal.com]

See, this seems trivial to me... and that's making me doubt my answer. I'm a gonna say down, assuming the difference was big enough/instruments fine enough to measure the difference.

I'm just-a-thinkin' that before sinking, volumetric displacement is caused by boat + lead weight + air inside boat but not inside lead weight. And that after sinking, volumetric displacement is caused by boat + lead weight and thus, the volume corresponding to the air which had filled the boat (but not the lead weight) will no longer be displacing water, so the water will fall a little.

Of course, in reality, there are spills and pumps in pools to ensure the water level stays relatively constant, so I'm going to guess we're talking a less mechanised pool.

So, am I a blind idiot? This seemed far too easy for a conundrum, which makes me doubtful of my answer.

[sps.livejournal.com]

And the altitude of the boat?

[denizsarikaya.livejournal.com]

Altitude of the boat above water level, you mean? I was basically considering volumetric displacement of a boat full of water versus a boat full of air. That's what I was thinking of.

[sps.livejournal.com]

No, I mean the altitude of the boat above the datum (sea level, whatever).

[denizsarikaya.livejournal.com]

I was assuming, given the constraints, that was very close to zero (and the boat was possibly shaped in a strange manner for this to occur). We could subtract out the volume of the boat which is above the datum, and ought, for accuraciy's sake, but my instincts say it would be less than the volume of the interior of the boat, unless the lead weight were friggin' huge.

[sps.livejournal.com]

Now I'm confused.

As the post's title indicates...

[denizsarikaya.livejournal.com]

Blame azrhey!

Re: As the post's title indicates...

[swestrup]

See clarification below.

[swestrup]

Here's a clarification: Before sinking, the boat essentially has zero projection above the level of the water in the pool. After sinking, its full of water...

And yes, Deniz's first instinct is wrong. Think about the law of buoyancy.

WHOOPS!

[swestrup]

I read Deniz' post wrong! I thought she was saying the level of the water would go up. She was correct after all, it goes down. This is because the volume displaced by an (almost) submerged object is equal to the volume of the same weight of water. After sinking, the boat only displaces its own volume + volume of lead weight, which MUST be less than the volume of the same weight of water, or the thing would never have floated at all...

Re: WHOOPS!

[denizsarikaya.livejournal.com]

Ahh, now I understand why you were invoking buoyancy.

And I was right! Yay!

For this, I break out a new user icon. Hah!

Re: WHOOPS!

[sps.livejournal.com]

Ah, now me whoops! I now notice that in this version the boat sinks. In my version (which is perhaps trickier), you toss the bowling ball over the side. Which is why I asked what happened to the level of the boat, see?